Jin, Zhaorong and Marcolli, Matilde (2014) Endomotives of toric varieties. Journal of Geometry and Physics, 77 . pp. 48-71. ISSN 0393-0440. doi:10.1016/j.geomphys.2013.12.006. https://resolver.caltech.edu/CaltechAUTHORS:20140401-134330780
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Abstract
We construct endomotives associated to toric varieties, in terms of the decomposition of a toric variety into torus orbits and the action of a semigroup of toric morphisms. We show that the endomotives can be endowed with time evolutions and we discuss the resulting quantum statistical mechanical systems. We show that in particular, one can construct a time evolution related to the logarithmic height function. We discuss relations to F_1-geometry.
| Item Type: | Article | ||||||||||||
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| Additional Information: | © 2014 Elsevier B.V. Received 4 October 2013. Received in revised form 10 December 2013. Accepted 14 December 2013. Available online 21 December 2013. This paper is based on the results of the first author’s summer research project, supported by a Summer Undergraduate Research Fellowship at Caltech. The second author acknowledges support from NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. | ||||||||||||
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| Subject Keywords: | Noncommutative geometry; Endomotives; Quantum statistical mechanical systems; Toric varieties; Height functions | ||||||||||||
| DOI: | 10.1016/j.geomphys.2013.12.006 | ||||||||||||
| Record Number: | CaltechAUTHORS:20140401-134330780 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20140401-134330780 | ||||||||||||
| Official Citation: | Zhaorong Jin, Matilde Marcolli, Endomotives of toric varieties, Journal of Geometry and Physics, Volume 77, March 2014, Pages 48-71, ISSN 0393-0440, http://dx.doi.org/10.1016/j.geomphys.2013.12.006. (http://www.sciencedirect.com/science/article/pii/S0393044013002301) | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 44582 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||
| Deposited On: | 01 Apr 2014 21:04 | ||||||||||||
| Last Modified: | 10 Nov 2021 16:53 |
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